1. What is the exponential distribution
Suppose the random variable X has a density function of the following form, then X is said to obey the exponential distribution with parameter θ, denoted as X~EXP(θ).
The distribution function of the exponential distribution is:
2. Expectation and variance of exponential distribution
①Mathematical expectation
If X obeys the exponential distribution with parameter λ (λ>0), then the mathematical expectation of the exponential distribution X~EXP(θ): λ
② variance
Let X obey the exponential distribution whose parameter is λ (λ>0), and the variance of the exponential distribution X~EXP(θ): λ^2.
To sum up, the probability density functions and graphs of the exponential distribution, uniform distribution and normal distribution that we often encounter are as follows:
